Non-linear stability in photogravitational non-planar restricted three body problem with oblate smaller primary

Details Non-linear stability in photogravitational non-planar restricted three body problem with oblate smaller primary Non-linear stability in photogravitational non-planar restricted three body problem with oblate smaller primary

2011-09-20

arxiv.org/abs/1109.4206v1

Mathematics

Dynamical Systems

Accepted for publication in Astrophysics & Space Science

Scientific paper

We have discussed non-linear stability in photogravitational non-planar restricted three body problem with oblate smaller primary. By photogravitational we mean that both primaries are radiating. We normalised the Hamiltonian using Lie transform as in Coppola and Rand (1989). We transformed the system into Birkhoff's normal form. Lie transforms reduce the system to an equivalent simpler system which is immediately solvable. Applying Arnold's theorem, we have found non-linear stability criteria. We conclude that $L_6$ is stable. We plotted graphs for $(\omega_1, D_2).$ They are rectangular hyperbola.

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